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• Differential calculus
  ...umn. One can also watch the sign of the differences of $A$; the values are increasing when the ''difference'' is positive! These are the points where the differe Furthermore, examining the graph reveals that the function is increasing where the slopes of the tangent lines are positive and decreasing where the
  84 KB (14,321 words) - 00:49, 7 December 2018
• Classes of functions
  When an object is moving up, we also say that its altitude is ''increasing'' and then, when its falling down, the altitude is ''decreasing''. We apply ...ning is very clear. However, both are imprecise. Even though we understand increasing functions as ones with graphs rising and decreasing functions as one with g
  143 KB (24,052 words) - 13:11, 23 February 2019
• Calculus exercises: part I
  *how fast is the level increasing? * monotonicity (increasing/decreasing),
  49 KB (8,436 words) - 17:14, 8 March 2018
• Precalculus
  *if $x$ is increasing, then $y$ is increasing; 1&1&\text{ increasing?}\\
  100 KB (16,148 words) - 20:04, 18 January 2017
• Calculus I, the discrete version
  '''Definition.''' A node function $f$ is called ''increasing on interval'' $[a,b]$ if ...rse, the function is increasing (or decreasing) on the interval when it is increasing (or decreasing) on each edge within the interval:
  64 KB (11,521 words) - 19:48, 22 June 2017
• Calculus of sequences
  As you can see, the behavior varies even within these two categories: increasing and decreasing. [[image:increasing and decreasing sequences.png| center]]
  113 KB (18,425 words) - 13:42, 8 February 2019
• Preview of calculus: part 2
  == Growth: Increasing/Decreasing Behavior == Function \( y=f(x) \) is ''increasing on interval'' \( (a, b) \) if for any given \( x_{1}, x_{2} \) in \( (a, b)
  19 KB (2,850 words) - 15:04, 19 March 2011
• Functions
  '''Example.''' An even simpler case is a list of numbers arranged in increasing order; then the task is easy: ...een calculated for you so that you can see patterns; for example, with $x$ increasing we see that
  151 KB (25,679 words) - 17:09, 20 February 2019
• Limits and continuity
  *increasing the pressure continuously in a closed container -- until it explodes, *increasing the temperature continuously of a piece of ice -- until it melts.
  107 KB (18,743 words) - 17:00, 10 February 2019
• Differential equations
  f(t,y)>0\ \Longrightarrow\ y \text{ is increasing};\\ Furthermore, every solution $y$ is decreasing (or increasing) throughout its domain. If we can demonstrate existence, every solution is
  64 KB (11,426 words) - 14:21, 24 November 2018
• Plotting the graph of a function
  #: * [[monotonicity|Increasing/decreasing]] ''Wrong:'' <del>So, $f$ increasing, on domain of $f$:</del>
  7 KB (1,132 words) - 17:34, 16 July 2011
• Preview of calculus: part 1
  ...reas by filling them with increasing number of rectangles or triangles and increasing the number of sides with each step. We can then calculate the area by calcu # If \( x \) is increasing, then \( y \) is increasing.
  10 KB (1,532 words) - 00:07, 2 May 2011
• Sequences and their limits
  ...ce Theorem).''' If a sequence is bounded and monotonic, i.e., it is either increasing, $a_n\le a_{n+1}$ for all $n$, or decreasing, $a_n\ge a_{n+1}$ for all $n$, is increasing. We have:
  64 KB (10,809 words) - 02:11, 23 February 2019
• Using derivative to study monotonicity
  This is helpful but what about ''[[increasing]]/decreasing'' behavior? m > 0 & \Rightarrow f \text{ increasing} \\
  4 KB (624 words) - 00:56, 16 July 2011
• Freshman's introduction to discrete calculus
  '''Theorem (Monotonicity).''' A node function is increasing (decreasing) on an interval if and only if its differential is positive (ne '''Theorem (Monotonicity).''' A node function is increasing (decreasing) on an interval if and only if its derivative is positive (nega
  42 KB (7,443 words) - 14:18, 1 August 2016
• Several variables
  Second, suppose that the price of sugar is increasing and then decreasing: What kind of dependencies are these? Increasing prices of the ingredients in creases the cost and ultimately the price of t
  76 KB (13,017 words) - 20:26, 23 February 2019
• Vector and complex variables
  Now, increasing the value of $q$ makes the graph of $y=f(x)$ shift upward and, eventually, ...o ''the signs of the real parts of their roots''. The signs will determine increasing and decreasing behavior of certain solutions. Once again, these are the pos
  113 KB (18,750 words) - 02:33, 10 December 2018
• Introduction to discrete calculus
  '''Theorem (Monotonicity).''' A $0$-cochain is increasing (decreasing) on an interval if and only if its exterior derivative is posit '''Theorem (Monotonicity).''' A $0$-cochain is increasing (decreasing) on an interval if and only if its derivative is positive (nega
  40 KB (6,983 words) - 19:24, 23 July 2016
• Differentiation
  As the width and the depth are increasing, so is the area of the rectangle. But the increase of the area cannot be ex *increasing slopes = tangents rotate counter-clockwise.
  82 KB (14,116 words) - 19:50, 6 December 2018
• Applications of integral calculus
  '''Exercise.''' Prove that if the density of the rod is strictly increasing (or decreasing), its center of mass cannot be in the center. '''Exercise.''' Find the center of mass of a rod with a linearly increasing density.
  103 KB (18,460 words) - 01:01, 13 February 2019

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